AS the nation's most ethnically diverse city - an uneasy amalgam of third world and first - Los Angeles has always been more salad bowl than melting pot. Now there's a thrust to see the mix doesn't become violently tossed.Some of the worst racial tensions since mandatory busing in the 1970s are forcing city and neighborhood officials to look for ways to calm hostilities among various ethnic groups. The issue has moved to the top of the city's political agenda. Last week, for instance, the mayor's office brokered a tenuous truce between Koreans and blacks in South-Central Los Angeles. In a housing project in Watts, Hispanics and blacks are meeting almost daily to foster greater communication and reduce crime in the wake of a fire that threatened to aggravate racial differences. New attempts are being made to enhance cultural sensitivity in schools. "This is a difficult period without a doubt," says Lionel Martinez of the Los Angeles County Human Relations Commission. "There is a lot of attention being given to the issue right now."

Third-world immigration Underlying the frictions are demographic changes virtually unparalleled in American history. Of the 14 million residents in the five-county Los Angeles area, 3 million arrived in the last decade. Unlike the great immigration patterns of the past, Los Angeles's influx has not been from Europe, but from third-world countries in Latin America and Asia, as well as from almost every corner of the globe. As New York writer David Rieff puts it in his new book "Los Angeles: Capital of the Third World:All that is certain is that the city coming into being is more fragmented and various than even the great immigrant Babels of late-19th-century America had been. New York, Chicago, Detroit, St. Louis - those cities had been anthologies of Europe, and L.A. is an anthology of the world." The result is a city, a mosaic, where Ethiopian food is sold near Armenian churches, where Japanese barbers advertise black hair styling, and where, according to one writer, the most common name given to a boy last year was Jose. Historian Kevin Starr calls it "the model of the unassimilated city." While the cultural diversity and international melange can be enriching, there is the danger of becoming an ethnic archipelago. Inevitably, tolerances get tested. This is particularly true as neighborhoods transform overnight and competition for scarce jobs and public services increases. South-Central Los Angeles, which includes Watts, was once the largest black enclave in the western United States. In the past decade, however, it has become a port of entry for Latinos. They now make up 45 percent of the population, and by 1993 experts believe Hispanics will outnumber blacks. Some of the most successful small businesses in the impoverished area are run by Koreans, which hasn't gone unnoticed by blacks. "You have a lot of economic differences and different economic roles evolving," says Paul Ong, an urban planner at the University of California at Los Angeles. "Some groups have a greater ability to take advantage of economic opportunities than others." Indeed, what may be most remarkable about Los Angeles is how little conflict has erupted. Some analysts still consider racial strife here far less than in some eastern US cities. "The untold story of the last 10 years has been people's coexistence with each other," says Mike Davis, author of the recent book "City of Quartz: Excavating the Future of Los Angeles.At the same time, in the past year we have seen the gathering of some really ominous signs."

Shootings and beatings Tensions surfaced with the police beating of black motorist Rodney King, and have escalated with subsequent allegations of brutality against members of the county Sheriff's Department. In the pact negotiated by Mayor Tom Bradley's office, black activists agreed to end a boycott of a Korean-American-owned store in South-Central. The store had been the target of a boycott since June 4, when owner Tae Sam Park fatally shot a black man. The owner was cleared in the incident by police. Under the pact, the store will be closed and offered for sale initially to black buyers. A "dispute resolution process" is being set up to resolve future conflicts. Despite the agreement, leaders of both communities acknowledge that mistrusts remain, and both sides are closely following the trial of another Korean-American charged in the shooting of a black, whom the clerk accused of stealing. In other areas, leaders are trying to tackle problems that transcend racial divisions. City Councilwoman Joan Milke Flores and others are organizing a multi-ethnic Watts community task force to deal with crime, gangs, economic development, and community services. Newly elected Councilman Mike Hernandez urges an expanded role for the Human Relations Commission. As he recently wrote in the Los Angeles Times: "Not since the debate over mandatory busing have race relations in Los Angeles received such attention. It is about time."